Many of those who fleeing the fighting have been forced to sleep in the open, and spend their days under the sun in temperatures set to reach 47C (117F) in the next few days.

Aid supplies are running dangerously low in overcrowded conditions. One newly opened camp, Amriyat al-Falluja, has only one latrine for 1,800 women, the NRC said.

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Tens of thousands of Falluja residents have fled to camps near the city

The government of Prime Minister Haider al-Abadi is already struggling to meet the needs of more than 3.4 million people across the country who have been displaced by conflict.

The IS group's self-styled Amaq news agency reported on Sunday that about 50 Iraqi troops had been killed and four army vehicles destroyed in "fierce fighting" with IS fighters near Falluja General Hospital in the north-east of the city.

Several civilians have been killed by militants while attempting to escape, including, on Monday, a two-year-old boy who was being carried by his mother.

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Media captionFalluja eyewitness: "There's been no food for 6 months"

Some residents were reportedly used as human shields by IS to slow the advance of government forces, who are being backed by air strikes from the US-led coalition.

IS militants had captured the northern city in January 2014 and held it for longer than any other city in Iraq or Syria - before the Iraqi army launched an operation to retake it.